where the contribution \(R(x, \hat{\mathbb {P}}_T, T)\)  is referred to as the regularization term.
For instance in the context of machine learning, c.f., Example REF , regularized ERM formulations typically take the form
\(\frac{1}{T} \sum _{t=1}^T L(f_{\theta }(X_t),Y_t) + \lambda _T \mu (\theta )\) 
where \(\lambda _T \in \mathbf {R}_+\)  and \(\mu : \Theta \rightarrow \mathbf {R}_+\) . Identifying \(\mu (\theta )\)  for instance as \(\Vert \theta \Vert _0\) , \(\Vert \theta \Vert _1\) , \(\Vert \theta \Vert _2\)  yields respectively sparse regression, LASSO [1]}, and Ridge [2]}, [3]}.
These methods have been shown to enjoy strong out-of-sample performance both in theory [4]}, [5]} as well as in practice.
